CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

This is a preview. Log in through your library . Abstract The results of this paper deal directly with the behavior of compositions of random probability generating functions. These results are then ...

What happened when a gambler asked for help from a mathematician? The formal study of Probability. Infinite Series is available to stream on pbs.org and the free PBS App, available on iPhone, Apple TV ...

This is a preview. Log in through your library . Abstract We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted ...

These are not the kinds of objects that concern Scott Sheffield. Sheffield, a professor of mathematics at the Massachusetts Institute of Technology, studies shapes that are constructed by random ...

Random walks constitute one of the most fundamental models in the study of stochastic processes, representing systems that evolve in a sequence of random steps. Their applications range from modelling ...

CATALOG DESCRIPTION: Advanced topics in random processes: point processes, Wiener processes; Markov processes, spectral representation, series expansion of random processes, linear filtering, Wiener ...